Doppler is a familiar phenomenon in which the frequency of a received signal appears to change as the radial velocity between the transmitter and receiver changes. Historically, this change in frequency has been modeled as a translation in frequency, but, as we will show, this model is not correct. The correct model is that Doppler results in a change of scale of the time axis of the signal.
Perhaps the first application of the Doppler equation was the measurement of the velocity at which stars are moving away from us. Under the big bang theory, this information can be used to estimate the distance of stars in the universe. In estimating the velocity of stars, light from an individual star was isolated and passed through a prism. The emission spectrum of an element, such as hydrogen, was identified and the apparent shift of one spectral emission component was measured to determine the star's velocity. In this case, the Doppler shift is easily measured since emission spectra consist of the sum of isolated sine waves at precise known frequencies.
With the invention of radar, it became necessary to resolve position and velocity. For radars operating with a fixed stable carrier frequency or a fixed stable pulse repetition frequency (PRF), the problem is similar to the star velocity problem. One may estimate the observed frequency of the carrier or PRF and obtain an estimate of the target velocity. This problem is again equivalent to estimation of the shift in frequency of a single sine wave. For the pulsed signal, the range may be estimated by calculating the delay between the time a pulse was transmitted and the time it was received. Range and velocity may therefore be simultaneously estimated from delay and Doppler. This is perhaps the first example of a Cross Ambiguity Function (CAF) process in which time delay and Doppler frequency are jointly estimated from the transmitted and received signals. For the radar problem, Doppler is universally modeled as a translation in frequency. The conventional CAF process provides acceptable results if the transmitted signal is a single sine wave, as it generally is with narrow band signals, however if the signal is not a sine wave the results obtained will not be accurate. To date, no methods have been developed to accurately measure non-sinusoidal signals.
U.S. Pat. No. 6,636,174, entitled “SYSTEM AND METHOD FOR DETECTION AND TRACKING OF TARGETS,” discloses a method of using a fractional Fourier transform in a CAF to track objects. This method is useful, for example, in radar and sonar systems to find position and estimate the velocity of signals. By altering computations in this method, the signals can be mapped to polar coordinates, as opposed to Cartesian, which is more accurate for certain types of signals. However, it does not address the problems solved by the present invention. U.S. Pat. No. 6,636,174 is hereby incorporated by reference into the present invention.
U.S. patent application Ser. No. 10/996,462, entitled “QUANTUM CROSS-AMBIGUITY FUNCTION GENERATOR,” discloses a method of applying quantum mechanics to the traditional cross-ambiguity function to achieve more accurate computations at increased bandwidths for both geo-location and radar applications. The constructed cross-ambiguity function generator, rather than having either an analog or digital construction, has a construction based on the properties of quantum physics based on electro-optical elements. Because the invention is based on different technology than existing systems, the advantages obtained by this invention will require significant investment by current users to implement. Further, it does not solve the problem addressed by the present invention. U.S. patent application Ser. No. 10/996,462 is hereby incorporated by reference into the specification of the present invention.
U.S. patent application Ser. No. 11/180,811, entitled “METHODS FOR DETECTION AND TRACKING OF TARGETS,” discloses a method of detecting and tracking targets. Specifically, signals are received and reflected from targets and processed to compute slices of the CAF. These slices are used to find the signal delay and Doppler shift associated with the targets, which facilitates tracking and targeting. This method attempts to solve the problem by only calculating slices of the CAF, thus simplifying computation. This does not result in the improvement in accuracy achieved by the present invention. U.S. patent application Ser. No. 11/180,811 is hereby incorporated by reference into the present invention.
Although prior art methods have been developed for locating and tracking targets, specifically in radar applications, these methods are primarily accurate only in narrowband applications. Methods that have attempted to account for problems beyond the narrow bandwidth case require extensive modifications to existing radar equipment, and therefore are impractical for users or manufacturers to implement from both a cost and efficiency standpoint. What is required in the art is a method of processing signals to determine position and velocity of a target accurately over a wide range of bandwidths.